Google only allows non-U2F 2FA methods (like TOTP) to be enabled AFTER enabling a hardware U2F device. And signing up without a working mobile number is impossible. Anyone who says that's not true hasn't actually tried in the last several years.
Nope, while I also did have TOTP before U2F (because it wasn't even a thing then), the rules changed to where if you don't have a phone number on your account, then you're required to enroll a U2F device before you can turn on TOTP.
